18 research outputs found
Embedding Invertible Languages with Binders - A Case of the FliPpr Language:St. Louis, MO, USA — September 27 - 28, 2018
Natural Deduction for Intuitionistic Non-Commutative Linear Logic
We present a system of natural deduction and associated term calculus for intuitionistic non-commutative linear logic (INCLL) as a conservative extension of intuitionistic linear logic. We prove subject reduction and the existence of canonical forms in the implicational fragment
Relating Natural Deduction and Sequent Calculus for Intuitionistic Non-Commutative Linear Logic
We present a sequent calculus for intuitionistic non-commutative linear logic (INCLL) , show that it satisfies cut elimination, and investigate its relationship to a natural deduction system for the logic. We show how normal natural deductions correspond to cut-free derivations, and arbitrary natural deductions to sequent derivations with cut. This gives us a syntactic proof of normalization for a rich system of non-commutative natural deduction and its associated -calculus. INCLL conservatively extends linear logic with means to express sequencing, which has applications in functional programming, logical frameworks, logic programming, and natural language parsing. 1 Introduction Linear logic [11] has been described as a logic of state because it views linear hypotheses as resources which may be consumed in the course of a deduction. It thereby significantly extends the expressive power of both classical and intuitionistic logics, yet it does not offer means to express sequencing. Th..